On eccentricity-based entropy measures for dendrimers

Huang, Rongbing; Siddiqui, Muhammad Kamran; Manzoor, Shazia; Ahmad, Shamim; Cancan, Murat

doi:10.1016/j.heliyon.2021.e07762

“…Indices are linked with total π-electron property and measured some entropies of trans-PD-(NH 2 )s lattice and metal-organic super-lattice structures, by using the different graph parameters, in [19]. Structures of dendrimers based on cyclotriphosphazene (N 3 P 3 ) are applied to the topics of balanced and computed the EPR temperature spectrum, discussed in [20]. First of all, the author computed eccentricity-based indices and their entropies.…”

Section: Introductionmentioning

confidence: 99%

Edge valency-based entropies of tetrahedral sheets of clay minerals

Tang

¹

,

Labba

²

,

Jamil

³

et al. 2023

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Humanity has always benefited from an intercapillary study in the quantification of natural occurrences in mathematics and other pure scientific fields. Graph theory was extremely helpful to other studies, particularly in the applied sciences. Specifically, in chemistry, graph theory made a significant contribution. For this, a transformation is required to create a graph representing a chemical network or structure, where the vertices of the graph represent the atoms in the chemical compound and the edges represent the bonds between the atoms. The quantity of edges that are incident to a vertex determines its valency (or degree) in a graph. The degree of uncertainty in a system is measured by the entropy of a probability. This idea is heavily grounded in statistical reasoning. It is primarily utilized for graphs that correspond to chemical structures. The development of some novel edge-weighted based entropies that correspond to valency-based topological indices is made possible by this research. Then these compositions are applied to clay mineral tetrahedral sheets. Since they have been in use for so long, corresponding indices are thought to be the most effective methods for quantifying chemical graphs. This article develops multiple edge degree-based entropies that correlate to the indices and determines how to modify them in order to assess the significance of each type.

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“…(1) Here, log is considered with base e. With the help of equation (1) modified for particular informational functions Φ(µν), where µν ∈ E(G), several informational functionalbased entropy measures were introduced in [51]; the explicit formulae of these entropies are given in table 2.…”

Section: Nomentioning

confidence: 99%

A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

Rani,

Fahad,

Hussain

et al. 2023

Meas. Sci. Technol.

1

0

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The study of different objects such as: properties of algebraic structures, analysis of chemical graph structures without experiment or understanding networks through topological indices (TIs) is among modern directions in graph theory. The analysis of different networks such as benes network, butterﬂy network, Hex-derived network and biswapped network by using TIs is one of the modern research ﬁelds. The storage and transferring of the data carrying certain information has always remained a modern world problem. The optoelectronic technology used in optical transpose interconnection systems (OTIS) is efﬁcient in outcome over an electrical system due to minimum power consumption and broad bandwidth. By combining the use of wireless and electrical technologies, OTIS has developed into a valuable network and boosted the efﬁciency of contemporary optoelectronic computers. A special type of OTIS is based on the biswapped network over path graph Pn, denoted by B(Pn). In this research work, a maximal twin-preserving subgraph of a biswapped network over path graph Pn is constructed. Moreover, the biswapped network B(Pn) and its constructed subgraph are explored through ev-degree and the ve-degree dependent TIs. A comparative analysis of the ev-degree and the ve-degree dependent TIs for B(Pn) and MT (B(Pn)) (a twin-preserving spanning subgraph of B(Pn)) is among the principal ﬁndings of present work. The analytical formulae, table and the graphical trends are used to describe a comparison between the TIs of the B(Pn) and its maximal twin-preserving subgraph. It is shown that the values of TIs only differ by a constant and does not depend on the value of n. Besides this, to analyse the complexity of MT (B(Pn)) through information functional based entropies, we deﬁne ve-degree and ev-degree based information functionals and compute formulae for ve-degree and ev-degree based entropies using information functionals. Numeric tables and graphs are also used to study complexity of MT (B(Pn)).

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“…In recent times, another approach which is a bit different in the literature, namely, using the concept of Shannon's entropy in terms of topological indices was introduced by Manzoor et al in [27]. Continuing their work, they also introduced eccentricity-based graph entropies [28,29] and bond additive graph entropies [30]. In this paper, the present authors formulated some new graph entropies, namely, neighborhood versions of graph entropies.…”

Section: Introductionmentioning

confidence: 96%

On Curvilinear Regression Analysis via Newly Proposed Entropies for Some Benzene Models

Liu

¹

,

Siddiqui

²

,

Manzoor

³

et al. 2022

Self Cite

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To avoid exorbitant and extensive laboratory experiments, QSPR analysis, based on topological descriptors, is a very constructive statistical approach for analyzing the numerous physical and chemical properties of compounds. Therefore, we presented some new entropy measures which are based on the sum of the neighborhood degree of the vertices. Firstly, we made the partition of the edges of benzene derivatives which are based on the degree sum of neighboring vertices and then computed the neighborhood version of entropies. Secondly, we made use of the software SPSS for developing a correlation between newly introduced entropies and the physicochemical properties of benzene derivatives. Our obtained results demonstrated that the critical temperature C T , critical pressure C P , and critical volume C V can be predicted through fifth geometric arithmetic entropy, second S K entropy, and fifth N D entropy, respectively. Other remaining physical characteristics include Gibb’s energy qℰ , log P , molar refractivity ℳℛ , and Henry’s law ℋℒ that can be predicted by using sixth N D entropy.

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On eccentricity-based entropy measures for dendrimers

Cited by 5 publications

References 44 publications

Edge valency-based entropies of tetrahedral sheets of clay minerals

Edge valency-based entropies of tetrahedral sheets of clay minerals

A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

On Curvilinear Regression Analysis via Newly Proposed Entropies for Some Benzene Models

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